Problem 2.41

A heat-conducting piston can freely move inside a closed thermally insulated cylinder with an ideal gas. In equilibrium the piston divides the cylinder into two equal parts, the gas tem perature being equal to \(T_{0}\). The piston is slowly displaced. Find the gas temperature as a function of the ratio \(\eta\) of the volumes of the greater and smaller sections. The adiabatic exponent of the gas is equal to \(\gamma\).